Ref.[1]} approaches the issue completely in terms of observables,
mostly the position and momentum observables. A spatial translation
as a change of relative position coordinates as seen from an inertial
(laboratory) frame \(A\)  to the relative position coordinates as seen
from another frame \(B\) , with a third system \(C\)  under consideration
is presented as a canonical transformation first explicitly given as
\(&&\hat{x}_{\!\scriptscriptstyle B}^{\scriptscriptstyle (A)} \longrightarrow -\hat{x}_{\!\scriptscriptstyle A}^{\scriptscriptstyle (B)} \;,\qquad \hat{p}_{\!\scriptscriptstyle B}^{\scriptscriptstyle (A)} \longrightarrow -(\hat{p}_{\scriptscriptstyle A}^{\scriptscriptstyle (B)}+\hat{p}_{\scriptscriptstyle C}^{\scriptscriptstyle (B)}) \;,\nonumber \\&&\hat{x}_{\!\scriptscriptstyle C}^{\scriptscriptstyle (A)} \longrightarrow \hat{x}_{\!\scriptscriptstyle C}^{\scriptscriptstyle (B)} - \hat{x}_{\!\scriptscriptstyle A}^{\scriptscriptstyle (B)} \;,\qquad \hat{p}_{\!\scriptscriptstyle C}^{\scriptscriptstyle (A)} \longrightarrow \hat{p}_{\scriptscriptstyle C}^{\scriptscriptstyle (B)} \;.\) 
